Ergodic properties of generalized Lüroth series

Jose Barrionuevo; Robert M. Burton; Karma Dajani; Cor Kraaikamp

Acta Arithmetica (1996)

  • Volume: 74, Issue: 4, page 311-327
  • ISSN: 0065-1036

How to cite


Jose Barrionuevo, et al. "Ergodic properties of generalized Lüroth series." Acta Arithmetica 74.4 (1996): 311-327. <>.

author = {Jose Barrionuevo, Robert M. Burton, Karma Dajani, Cor Kraaikamp},
journal = {Acta Arithmetica},
keywords = {ergodic properties; construction of generalized Lüroth series; transformations},
language = {eng},
number = {4},
pages = {311-327},
title = {Ergodic properties of generalized Lüroth series},
url = {},
volume = {74},
year = {1996},

AU - Jose Barrionuevo
AU - Robert M. Burton
AU - Karma Dajani
AU - Cor Kraaikamp
TI - Ergodic properties of generalized Lüroth series
JO - Acta Arithmetica
PY - 1996
VL - 74
IS - 4
SP - 311
EP - 327
LA - eng
KW - ergodic properties; construction of generalized Lüroth series; transformations
UR -
ER -


  1. [B] J. R. Brown, Ergodic Theory and Topological Dynamics, Academic Press, New York, 1976. Zbl0334.28011
  2. [BJW] W. Bosma, H. Jager and F. Wiedijk, Some metrical observations on the approximation by continued fractions, Indag. Math. 45 (1983), 281-299. Zbl0519.10043
  3. [CFS] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Grundlehren Math. Wiss. 245, Springer, New York, 1982. 
  4. [FS] C. Frougny and B. Solomyak, Finite beta-expansions, Ergodic Theory Dynamical Systems 12 (1992), 713-723. Zbl0814.68065
  5. [G] J. Galambos, Representations of Real Numbers by Infinite Series, Lecture Notes in Math. 502, Springer, Berlin, 1982. Zbl0322.10002
  6. [J] H. Jager, On decimal expansions, Zahlentheorie, Berichte aus dem Mathematische Forschungsinstitut Oberwolfach 5 (1971), 67-75. 
  7. [JdV] H. Jager and C. de Vroedt, Lüroth series and their ergodic properties, Indag. Math. 31 (1968), 31-42. Zbl0167.32201
  8. S. Kalpazidou, A. Knopfmacher and J. Knopfmacher, Lüroth-type alternating series representations for real numbers, Acta Arith. 55 (1990), 311-322. Zbl0702.11048
  9. S. Kalpazidou, A. Knopfmacher and J. Knopfmacher, Metric properties of alternating Lüroth series, Portugal. Math. 48 (1991), 319-325. Zbl0735.11035
  10. [K] C. Kraaikamp, A new class of continued fraction expansions, Acta Arith. 57 (1991), 1-39. Zbl0721.11029
  11. [Li] P. Liardet, MR: 93m:11077. 
  12. [Lu] J. Lüroth, Ueber eine eindeutige Entwickelung von Zahlen in eine unendliche Reihe, Math. Ann. 21 (1883), 411-423. 
  13. [Pa] W. Parry, On the β-expansions of real numbers, Acta Math. Acad. Sci. Hungar. 11 (1960), 401-416. Zbl0099.28103
  14. [Pe] O. Perron, Irrationalzahlen, de Gruyter, Berlin, 1960. 
  15. [R] V. A. Rohlin, Exact endomorphisms of a Lebesgue space, Izv. Akad. Nauk SSSR Ser. Mat. 24 (1960) (in Russian); English translation: Amer. Math. Soc. Transl. Ser. 2, 39 (1969), 1-36. 
  16. [Sa] T. Šalát, Zur metrischen Theorie der Lürothschen Entwicklungen der reellen Zahlen, Czech. Math. J. 18 (1968), 489-522. Zbl0162.34703
  17. [So] B. Solomyak, Personal communication with C. Kraaikamp, Seattle, July 9, 1991. 
  18. [V] W. Vervaat, Success Epochs in Bernoulli Trails with Applications in Number Theory, Math. Centre Tracts 42, Amsterdam, 1972. Zbl0267.60003
  19. [W] P. Walters, An Introduction to Ergodic Theory, Grad. Texts in Math. 79, Springer, New York, 1982. 

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